Development of New Dimension-Reduction Methods for Reliability, Simulation, and Design of Complex Engineering Systems

该研究项目的目标是为复杂工程系统的不确定性传播、可靠性分析和设计优化开发新的计算方法。 建议的工作将基于：（1）新的降维方法计算二阶矩特性的随机响应;（2）新的降维和基于矩的随机方法的可靠性分析;和（3）新的算法的可靠性为基础的/稳健的设计优化的结构和机械系统。 所提出的方法是新颖的，将能够解决高度非线性的输入输出变换;无限数量的随机变量或过程;和任意大的输入不确定性，但将准确地预测响应时刻和可靠性。 潜在的工程应用包括地面车辆的耐久性设计;航空航天结构的疲劳和断裂设计;以及微电子封装系统的设计。 从基本的观点来看，降维方法将为任意区域上的一般多维积分提供精确而有效的解。 因此，在基础科学和应用科学，这涉及不确定性和/或需要评估这样的积分，许多问题将解决的方法在这个项目中开发。 该项目创造的知识转移将通过以下方式进行：与行业的持续合作;在ASME会议上组织关于可靠性和设计的研讨会;同行评审的期刊出版物;在主要会议和机构上的演讲和出版物;以及学生教育。 教育目标包括招收一名女博士。来自代表性不足少数民族的学生;在升级设计和可靠性课程中使用该项目的软件工具;以及编写一本综合教科书。

The objective of this research project is to develop new computational methods for uncertainty propagation, reliability analysis, and design optimization of complex engineering systems. The proposed effort will be based on: (1) new dimension-reduction methods for calculating second-moment characteristics of random response; (2) new dimension-reduction and moment-based stochastic methods for reliability analysis; and (3) new algorithms for reliability-based/robust design optimization of structural and mechanical systems. The proposed methods are novel and will be able to address highly nonlinear input-output transformations; unlimited number of random variables or processes; and arbitrarily large uncertainty of input, yet will predict both response moments and reliability accurately. Potential engineering applications include ground vehicle design for durability; fatigue and fracture design of aerospace structures; and design of microelectronics packaging systems. From a fundamental point of view, the dimension-reduction methods will provide an accurate and efficient solution to a general multi-dimensional integral over an arbitrary region. Hence, many problems in basic and applied sciences, which involve uncertainty and/or require evaluation of such integrals, will be solved by the methods developed in this project. The transfer of knowledge created by this project will take place through continued collaboration with industries; organization of symposia on reliability and design in ASME conferences; peer-reviewed journal publications; presentations and publications at major conferences and institutions; and student education. The educational goals comprise recruitment of a female Ph. D. student from underrepresented minority; implementation of software tools from this project in upgrading design and reliability courses; and authoring a comprehensive textbook.